I'm going to try to answer this from the writings on Ādi Śaṅkaracharya himself, and Śrīharṣa, a 12th-century Indian philosopher of Advaita Vedanta. Although his main center of critique was the Nyāya Darśan, however, Vijñānavāda isn't left out from the maestro's sharp reasonings, as we'll see.
1. Doesn't this go against the Advaitic idea of unreality of the external world?
As expounded here: Chapter 8. Śaṅkara Bhagavatpāda
Śaṅkara does not deny the validity of the known world as is generally thought. He accepts it but denies any original and separate existence for it, apart from and independent of Brahman.
He propagated three levels of truth, viz.,
- the Vyāvahārika Satya,
- the Prātibhāsika Satya and
- the Pāramārthika Satya.
Thus, the relative existence of the known world is not a total non-existence, like the son of a barren woman. Some measure of reality is given even to the phantom world of apparitions and dreams called Prātibhāsika Satya. The reality, being the plenary unconditional experience beyond the concepts and the categories of the mind, it is only the Śruti that can testify to its truth. All the same a rational explanation of the contradictions that we see in the relative world becomes necessary and this reconciliation of the two seemingly irreconcilable principles is done in terms of the doctrine of Māyā and Adhyāsa (Superimpostion).... The three ideas of truth, illusion and absolute non-existence, or in other words, ‘Satya’, ‘Mithyā’, and ‘Atyantāsat’, are expounded with the illustrations of the ‘Supreme one’, the serpent in the rope, and the son of a barren woman, etc.
Thus Śaṅkara’s definition of the world is not that of an illusionist as has been misrepresented by some, who denies reality to that which is seen and felt by us, in our daily activities. Śaṅkara has never said so. On the other hand, he reconciles our various experiences by the device of the various levels of truth.
2. Or is there some fundamental difference between the Vijñānavāda's 'non-reality' and the Advatic 'non-reality'?
Sri-Harsha starts with the thesis that none of our cognitions ever require any proof for their validity. The Advaita of Sankara and the idealistic school of Buddhism (Vijnanavada) differs in this that while the latter holds that everything including the cognition is unreal and indeterminable, the former holds that knowledge is identical with Reality from which the entire universe proceeds and, therefore, knowledge is real and the entire universe is indeterminable. It is this distinction between the Advaita school of Sankara and the idealistic school of Buddhism that the critics of Advaita often overlook when they charge that Advaita is akin to the Vijnana-vada school of Buddhism. Indefinability is the very nature of the objects of the world. Sri-Harsha contends that no amount of ingenuity can succeed in defining the nature of the objects which have no definable existence. All the definitions of the objects put forward by the Nyaya writers are shown to be faulty even according to the canons of logical discussions and definitions accepted by the Naiyayika. Sri-Harsha contends that no definitions of the phenomenal world are possible and that the world of phenomena and all our so-called experiences of it is indefinable. So the Advaitins could affirm that the indeterminable nature of the world is proved. Sri-Harsha does not believe in the reality of his arguments. He employs them without any assumption of their reality or unreality. If the arguments of Sri-Harsha are proved to be unreal then that establishes his own contention that nothing except the self-luminous Brahman is real. Sri-Harsha is interested only in refuting the definitions of the Naiyayikas. And, his conclusion is that the manifold world of our experience is indefinable and the one Brahman is absolutely and ultimately real.
Chapter 19. Śrī-harṣa
Quoting from this book - Preceptors of Advaita compiled by T.M.P. Mahadevan
SRI KANCHI KAMAKOTI SANKARA MANDIR
Also, it would be extremely helpful if I could get a quote from Shankaracharya or other Advaita Philosophers regarding this specific issue.
As elaborated in the '2nd' part of the answer Śrī Harṣa categorically did differentiate between Buddhism's śūnyavāda/anātmavāda and the svayaṃprakāśavāda of the Advaita Vedanta.
I'm providing the direct quote by Śrī Harṣa which he makes in his celebrated work - Khaṇḍana-khaṇḍa-khādya (literally means ‘sweets of refutation’)
॥ इति स्वप्रकाशवादः ॥ शून्यवाद और स्वयंप्रकाशवाद में भेद ।
एवं च सति सौगतब्रह्मवादिनोरयं विशेषो यदादिमः सर्वमेवानिर्वचनीर्य
वर्णयति तदुक्तं भगवता लङ्कावतारे "बुद्धया विविच्यमानानां स्वभावो
नावधार्यते। अतो निरभिलप्यास्ते निःस्वभावाश्च देशिताः” इति
विज्ञानव्यतिरिक्तं पुनरिदं विश्वं सदसयां विलक्षणं ब्रह्मवादिनः
संगिरन्ते । तथाहिनेदं सद्भवितुमर्हति, वक्ष्यमाणदूषणग्रस्तत्वात् ।
नाप्यसदेव, तथा सति लौकिकविचारकाणां सर्वव्यवहारव्याहत्यापत्तेः ॥१॥
- English translation of the above-quoted Sanskrit text by Ganganath Jha from here.
- The difference between the Bauddha and the Vedantin then comes to this -- the Bauddha regards everything, without exception, as anirvachanīya, i.e, undefinable; as (Lord) Buddha himself has declared in the Latikavatara Sutra (II. 173)—
“when we come rationally to examine things, we cannot ascertain the nature of anything; hence all things must be declared to be undefinable and devoid of any assignable nature or character". __ The Vedantins on the other hand declare that this entire
Universe, with the exception of Cognition or Consciousness, is neither absolutely real nor absolutely unreal. It cannot be absolutely real, because this view is beset by difficulties which we shall point out later on; nor can we regard it as absolutely unreal since this would strike at the root of all empirical thought, speech, and action of intelligent men of the world.